Interferometric topological metrology with pre-established reference scale

ABSTRACT

A method is described that involves measuring a first set of interferometer fringe line disturbances against pre-determined measurement scale information in order to generate a first set of profiles that describe the topography of a sample that is placed upon a sample stage associated with the interferometer. The first set of profiles map to traces that run over a first axis of the sample and the sample stage. The traces have a recognized spacing between one another along a second axis of the sample and the sample stage. The method also involves adjusting the relative position of the traces to the sample so as to create a second set of fringe line disturbances. The method also involves measuring, the second set of interferometer fringe line disturbances against the pre-determined measurement scale information in order to generate a second set of profiles that describe the topography of the sample. The method also involves interleaving the first set of profiles and the second set of profiles to create a topography description of the sample that has a resolution along the second axis that is smaller than the spacing.

FIELD OF INVENTION

The field of invention relates generally to measurement techniques; and,more specifically, to a pre-established reference scale for aninterferometric topological measurement.

BACKGROUND

1.0 Basic Interferometry

Interferometry involves the analysis of interfering waves in order tomeasure a distance. Interferometers, which are measurement tools thatperform interferometry, typically reflect a first series of opticalwaves from a first reflecting surface; and, reflect a second series ofoptical waves from a second reflecting surface. The first and secondseries of waves are subsequently combined to form a combined waveform. Asignal produced through the detection of the combined waveform is thenprocessed to understand the relative positioning of the reflectivesurfaces. FIG. 1 shows an embodiment of a type of interferometer that isoften referred to as a Michelson interferometer.

Referring to FIG. 1, a light source 101 and splitter 102 are used toform a first group of light waves that are directed to a referencemirror 104; and, a second group of light waves that are directed to aplane mirror 103. The splitter 102 effectively divides the light 106from the light source 101 in order to form these groups of light waves.Typically, the splitter 102 is designed to split the light 106 from thelight source 101 evenly so that 50% of the optical intensity from thelight source 101 is directed to the reference mirror 104 and 50% of theoptical intensity from the light source 101 is directed to the planemirror 103.

At least a portion of the light that is directed to the plane mirror 103reflects back to the splitter 102 (by traveling in the +z directionafter reflection); and, at least a portion of the light that is directedto the reference mirror 104 reflects back to the splitter 102 (bytraveling in the −y direction after reflection). The reflected lightfrom the reference mirror 104 and plane mirror 103 are effectivelycombined by the splitter 102 to form a third group of light waves thatpropagate in the −y direction and impinge upon a detector 105. Theoptical intensity pattern(s) observed by the detector 105 are thenanalyzed in order to measure the difference between the distances d1, d2that exist between the plane mirror 103 and the reference mirror 104,respectively.

That is, for planar wavefronts, if distance d₂ is known, distance d₁ canbe measured by measuring the intensity of the light received at thedetector 105. Here, according to wave interference principles, ifdistance d₁ is equal to distance d₂; then, the reflected waveforms willconstructively interfere with one another when combined by the splitter102 (so that their amplitudes are added together). Likewise, if thedifference between distance d₁ and distance d₂ is one half thewavelength of the light emitted by light source 101; then, the reflectedwaveforms will destructively interfere with one another when combined bythe splitter 102 (so that their amplitudes are subtracted from oneanother).

The former situation (constructive interference) produces a relativemaximum optical intensity (i.e., a relative “brightest” light) at thedetector 105; and, the later situation (destructive interference)produces a relative minimum optical intensity (i.e., a relative“darkest” light). When the difference between distance d1 and distanced2 is somewhere between zero and one half the wavelength of the lightemitted by the light source 101, the intensity of the light that isobserved by the detector 105 is less than the relative brightest lightfrom constructive interference but greater than the relative darkestlight from destructive interference (e.g., a shade of “gray” between therelative “brightest” and “darkest” light intensities). The precise“shade of gray” observed by the detector 105 is a function of thedifference between distance d₁ and distance d₂.

In particular, the light observed by the detector 105 becomes darker asthe difference between distance d₁ and distance d₂ depart from zero andapproach one half the wavelength of the light emitted by the lightsource 101. Thus, the difference between d1 and d2 can be accuratelymeasured by analyzing the optical intensity observed by the detector105. For planar optical wavefronts, the optical intensity should be“constant” over the surface of the detector 105 because (according to asimplistic perspective) whatever the difference between distance d₁ andd₂ (even if zero), an identical “effect” will apply to each optical pathlength experienced by any pair of reflected rays that are combined bythe splitter 102 to form an optical ray that is directed to the detector105.

Here, note that the 45° orientation of the splitter 102 causes thereference mirror directed and plane mirror directed portions of light totravel equal distances within the splitter 102. For example, analysis ofFIG. 1 will reveal that the reference mirror and plane mirror directedportions of ray 107 travel equal distances within splitter 102; and,that the reference mirror and plane mirror directed portions of ray 108travel equal distances within splitter 102. As all light rays travelingto detector 105 from splitter 102 must travel the same distance d3, itis clear then that the only difference in optical path length as betweenthe plane mirror and reference mirror directed portions of light (thatare combined to form a common ray that impinges upon the detector 105),must arise from a difference between d1 and d2; and; likewise, forplanar wavefronts, a difference between d1 and d2 should affect alllight rays impingent upon detector 105 equally. As such, ideally, thesame “shade of gray” should be observed across the entirety of thedetector; and, the particular “shade of gray” can be used to determinethe difference between distance d1 and d2 from wave interferenceprinciples.

2.0 Interferometer Having A “Tilted” Reference Mirror

Referring to FIG. 2, when the reference mirror 204 is tilted (e.g., suchthat θ is greater than 0° as observed in FIG. 2), the optical intensityobserved at the detector 205 departs from being uniform across thesurface of the detector 205 because the differences in optical pathlength as between plane mirror 203 and reference mirror 204 directedportions of light are no longer uniform. Better said, the “tilt” in thereference mirror 204 causes variation in optical path length amongst thelight waves that are directed to the reference mirror 204; which, inturn, causes variation in the optical intensity observed at the detector205.

Here, as wave interference principles will still apply at the detector205, the variation in optical path length that is introduced by thetilted reference mirror 204 can be viewed as causing optical path lengthdifferences experienced by light that impinges upon the detector 202 toeffectively progress through distances of λ/2, λ, 3λ/2, 2λ, 5λ/2, 3λ,etc. (where λ is the wavelength of the light source). This, in turn,corresponds to continuous back and forth transitioning betweenconstructive interference and destructive interference along the z axisof the detector 205. FIG. 3 a shows an example of the optical intensitypattern 350 observed at the detector 305 when the reference mirror of aninterferometer is tilted (as observed in FIG. 2).

Here, notice that the optical intensity pattern 350 includes relativeminima 352 a, 352 b, and 352 c; and, relative maxima 351 a, 351 b, 351c, and 351 d. The relative minima 352 a, 352 b, and 352 c, which shouldappear as a “darkest” hue within their region of the detector 305, arereferred to as “fringe lines”. FIG. 3 b shows a depiction of the fringelines that appear on a detector when the reference mirror of aninterferometer is tilted. Here, ideally, fringe lines that run along thex axis will repeatedly appear as one moves across the z axis of thedetector. The separation of the fringe lines is a function of both thewavelength of the light source and the angle at which the referencemirror is tilted. More specifically, the separation of the fringe linesis proportional to the wavelength of the light source and inverselyproportional to the angle of the tilt. Hence, fringe line separation maybe expressed as ˜λ/θ.

FIGURES

The present invention is illustrated by way of example and notlimitation in the figures of the accompanying drawings.

FIG. 1 shows an interferometric measurement system;

FIG. 2 shows an interferometric measurement system having a tiltedreference mirror;

FIG. 3 a shows a depiction of an optical intensity pattern that resultswhen the reference mirror of an interferometric is tilted;

FIG. 3 b shows the fringe lines observed at the detector of aninterferometer when its reference mirror is tilted;

FIG. 4 a shows how a fringe line maps to a particular y axis locationalong the sample stage;

FIG. 4 b shows perturbations inflicted upon the fringe lines of aninterferometer having a tilted reference mirror as a result of a samplebeing placed upon the inteferometer's sample stage;

FIG. 5 shows an embodiment of a methodology that may be used to generatea topographical description of a sample;

FIG. 6 shows an embodiment of a methodology for establishing a referencescale against which fringe line changes are to measured;

FIG. 7 a shows a “top view” of a reference standard;

FIG. 7 b shows a slanted view of the reference standard of FIG. 7 a;

FIG. 7 c shows a representation of the image that appears at thedetector of an interferometer having a tilted reference mirror when areference standard is placed on the sample stage;

FIG. 8 shows an embodiment of a methodology for aligning fringe lines tothe reference lines of a reference standard that is placed on the samplestage of an interferometer;

FIG. 9 a shows neighboring fringe lines on a CCD array detector for aninterferometer having a tilted reference mirror;

FIG. 9 b shows the disturbance caused to one of the fringe lines when asample having a height of λ/4 is placed along its optical path;

FIG. 10 a shows an embodiment of an interferometer having a tiltedreference mirror that measures sample topography against apre-established measurement scale;

FIG. 10 b shows an embodiment of a computing system;

FIG. 11 a shows a methodology for detecting fringes;

FIG. 11 b shows a circuit that may be used to detect fringe lines;

FIG. 11 c shows signals that are relevant to the operation of thecircuit of FIG. 11 b;

FIG. 12 a shows an embodiment of fringe tracings that are used to form apre-established measurement scale;

FIG. 12 b shows a perspective of a pre-established measurement scale;

FIG. 13 shows an embodiment of the disturbances that are caused to thefringe tracings of FIG. 12 a when a sample is introduced to aninterferometer;

FIG. 14 shows topography information of the sample that is extractedfrom an analysis of the fringe tracings of FIGS. 12 a and 13;

FIG. 15 shows an embodiment of a circuit that may be used to implementthe topography measurement unit of FIG. 10A;

FIG. 16 a shows a depiction of a “new” pattern of fringe tracings aftera sample is moved along the y axis;

FIG. 16 b shows a depiction of the “new” relative positioning of thesample that corresponds to the “new” fringe pattern tracings observed inFIG. 18 a;

FIG. 17 shows a depiction of a topography description of a samplederived from the fringe tracings observed in FIGS. 13 and 18 a;

FIG. 18 a shows an exemplary depiction of a reflectivity vs. lightsourcewavelength suitable for characterizing sample composition;

FIG. 18 b shows a first methodology that may be used to generate areflectivity vs. lightsource curve;

FIG. 18 c shows a second methodology that may be used to generate areflectivity vs. lightsource curve;

FIG. 19 a shows an exemplary depiction of fringe line disturbances thatexpand outside their associated reference field;

FIG. 19 b shows an exemplary depiction of a sample that could cause thefringe line disturbance patterns observed in FIG. 19 a;

FIG. 20 shows a methodology that may be used to follow a fringe linethat is disturbed beyond its associated reference field;

FIG. 21 a shows a methodology that may be used to follow a particularedge of a fringe line disturbance that is disturbed beyond itsassociated reference field;

FIG. 21 b is an exemplary depiction that applies to the following of asegment of the downward sloped edge of fringe line 1951 b of FIG. 19;

FIG. 21 c is an exemplary depiction that applies to the following of asegment of the upward sloped edge of fringe line 1951 b of FIG. 19.

DETAILED DESCRIPTION

As described below, principles of interferometry are utilized so that anaccurate description of the surface topology of a sample can be gained.More specifically, fringe line disturbances observed on the detector ofan interferometer (that are caused by the introduction of the sample tothe interferometer) are measured against a pre-established referencescale. As a result, the height of the sample can be mapped to specificlocations on the surface of the sample; which, in turn, allows for thedevelopment of a precise description of the topographical nuances of thesample.

1.0 Mapping of Detector Surface Location to Sample Stage Surface Trace

FIGS. 4 a and 4 b together show an embodiment of the “mapping” thatexists between the fringe lines that appear on the detector 405 of aninterferometer having a tilted reference mirror; and, the corresponding“traces” of these fringe line on a sample stage 403. Here, the samplestage 403 may have a reflective coating so that, by itself, it behavesthe same as (or at least similar to) the plane mirror 103 discussedabove in the background section. Referring to FIG. 4 a, for a 45°splitter 402 orientation, each fringe line effectively “maps to” a tracethat runs parallel to the x axis at a specific y axis location on thesample stage 403. That is, each fringe line “maps to” its 90° reflectionoff of the splitter 402 and toward the sample stage 403. Here, if the zaxis positioning of a fringe line on the detector (e.g., z axis positionz_(k)) is projected to the splitter 402 (via projection 491) and“reflected” off of the splitter 402 at an angle of 90° (to formprojection 492) to the sample stage 403, the projection 492 to thesample stage 403 will impinge upon a particular y axis location of thesample stage 403 (e.g., Y_(k) as observed in FIG. 4 a).

Referring to FIG. 4 b, when a sample whose topography is to be measured(e.g., sample 460) is placed upon the sample stage 403, disturbances tothe fringe lines (as compared to their original appearance prior to theappearance of the sample) will appear. For each fringe line, thedisturbance(s) follow the topography of the sample 460 along its “mappedto” trace that runs parallel to the x axis along the sample stage 403 asdescribed in FIG. 4 a. Thus, referring to FIG. 4 b, the disturbance offringe lines 451 b, 451 c, 451 d on the detector 405 “map to” traces 452b, 452 c, 452 d, respectively on the sample stage 403. Since the sample460 does not cover traces 452 a, 452 e of the sample stage 403, fringelines 451 a and 451 e remain undisturbed upon the detector 403.

2.0 Interferometry Measurement Technique Employing a Pre-EstablishedMeasurement Scale

FIG. 5 shows an embodiment of a methodology for developing a descriptionof the topography of a sample by measuring optical fringe linedisturbances (that occur in response to a sample being placed upon thesample stage of an interferometer) against a pre-established measurementscale. According to the approach of FIG. 5, a measurement scale (whichmay also be referred to as a reference scale, scale, etc.) is firstestablished 501. The measurement scale can be viewed as akin to a rulerthat is used to measure fringe line disturbances. As such, when a sampleis introduced to the interferometer and an interferometric image of thesample is produced 502, the topography of the sample can be preciselyunderstood by way of measuring the fringe lines against thepre-established measurement scale 503.

Better said, the disturbances experienced by the fringe lines inresponse to the sample being introduced to the interferometer can beprecisely translated into sample height along known locations in the xyplane of the sample stage. The pre-establishment of a reference scalenot only allows for highly precise surface topography descriptions butalso allows for efficiently produced surface topography descriptions(e.g., in terms of equipment sophistication and/or time expended). FIGS.6 through 9 a, 9 b relate to the establishment of a measurement scale;and, a discussion of each of these Figures follows immediately followsbelow.

3.0 Establishment of Measurement Scale

FIG. 6 shows a methodology for establishing a measurement scale. Notethat the methodology of FIG. 6 includes an “accuracy in the xy plane”component 610; and, an “accuracy in the z direction” component 611.Here, referring to FIGS. 4 b and 6, setting the accuracy in the xy plane610 corresponds to producing a measurement scale from which precisepositions along the plane of the sample stage 403 can be deduced.Likewise, setting the accuracy in the z direction 611 corresponds toproducing a measurement scale from which precise changes in thetopographical profile of the sample 460 can be tracked. By combinationof establishing accuracy in the xy plane as well as in the z direction,a three dimensional description of the sample can be generated thatprecisely tracks sample height (in the z direction) across a pluralityof x and y positions over the surface of the sample 460 and the samplestage 403.

According to the methodology of FIG. 6, accuracy in the xy plane can beestablished by aligning 610 the fringe lines that are observed on thedetector 405 to be equidistant with those of a calibration standard(noting that, with respect to FIG. 4 b, the calibration standard ispresented upon the stage 403 rather than a sample 460). Once the fringelines are aligned 610, a “per pixel unit of sample height measurement”parameter is calculated 611.

Here, an array of optically sensitive devices (e.g., an array of chargecoupled devices (CCDs)) may be used to implement the detector 405. Eacharray location may be referred to as a “pixel”. Because of the array,each optically sensitive device that a disturbed fringe line featureruns across will correspond to a unique x,y,z position (above thesurface plane of the detector 405) along the topography of the sample.Better said, the setting of the accuracy in the xy plane 610 allows adetector pixel to be “mapped” to a specific position in the xy plane ofthe sample stage. As such, should a fringe line become disturbed uponintroduction of a sample to the interferometer, the distance(s) that thefringe line moves upon the detector from its original, undisturbed pixellocations will correspond to the height of the sample at thoseparticular x,y sample stage positions that the original, undisturbedpixel locations mapped to.

Thus, as each of the optically sensitive devices that make up the arrayconsume a quantifiable amount of surface area on the plane of thedetector 405 (i.e., each pixel has a “size”), when measuring the expanseof a fringe line disturbance, each pixel will typically correspond to aparticular unit of “height” above the sample stage as measured along thez axis of the detector. Better said, recalling from the discussion ofFIG. 4 b that fringe line disturbances result from the placement of asample 460 on the interferometer sample stage 403, a specific change infringe line position can be translated to a specific sample height.

Here, the height of the sample can be deduced from the distance alongthe z axis that a fringe line section or portion will “move” along thesurface of the detector 405 (i.e., be disturbed) by the introduction ofthe sample 460 to the interferometer. As such, each pixel position canbe correlated to a specific unit distance along the z axis above thesurface of the sample stage 403; which, in turn, can be used to “figureout” the height of the sample above the sample stage 403. Morediscussion of this topic is provided further below with respect to FIGS.9 a and 9 b.

For purpose of explaining FIG. 6, however, the amount of unit distancealong the z axis above the sample stage 403 that a pixel represents canbe referred to as the “per pixel unit of sample height measurement” 611.For example, if the per pixel unit of sample height measurement is 20nm; and, a fringe line is observed to move 3 pixels along the z axis ofthe detector 405 when a sample is placed upon the sample stage; then,the sample height will be calculated as 60 nm. As a side note, eachpixel's optically sensitive device may be configured so that the opticalintensity that impinges upon its unique xz position of the detector 405is provided as a digital output. For example, each optically sensitivedevice in the array may be configured to provide a byte of informationthat represents the optical intensity observed at its particular, uniquexz location on the detector 405 surface.

Once the fringe lines have been aligned 610 to a calibration standardand the per pixel unit of sample height measurement is calculated 611, apre-established measurement scale can be formed by recording 612: 1)information related to the mapping of the detector's fringe lines to thesample stage 403 without a sample being placed on the sample stage (e.g,for each fringe line observed on the detector 405 when a sample is notplaced upon the sample stage: a) recording its x,z pixel locations onthe detector 405; and b) recognizing how the x,z locations on thedetector 405 map to x,y locations upon the sample stage 403); and, 2)the per pixel unit of sample height measurement.

Note that a sample is the “thing” whose surface topography is to bemeasured. According to the methodology of FIG. 6 then, once theundisturbed fringe lines have been aligned and their mapping positionrecorded; and, once, the per pixel unit of sample height measurement iscalculated and recorded, information has been stored 612 that issuitable for creating a measurement scale that can be used to measurethe topography of a sample.

3.1 Aligning Fringe Lines with a Calibration Standard

FIGS. 7 a through 7 c and FIG. 8 relate to a technique for aligning 610the fringe lines to a calibration standard as discussed in FIG. 6. Acalibration standard is a device having markings that are spaced apartwith a high degree of precision. For example, the National Institute ofStandards and Technology (NIST) provide calibration standards havinglengthwise gratings that are spaced evenly apart (e.g., where eachgrating is spaced 1 μm apart). An example of a calibration standard isobserved in FIGS. 7 a and 7 b. Here, each grating (or other marking) isspaced evenly apart by a distance of “Y” on the surface of thecalibration standard. FIG. 7 a shows a “top down” view of an exemplarycalibration standard 700 while FIG. 7 b shows a slanted view of anexemplary calibration standard 700.

FIG. 7 c shows a representation 701 of the optical image that appears onthe detector of an interferometer having a tilted reference mirror whenthe calibration standard is placed on its sample stage. Here, theoptical image will include images of the markings of the calibrationstandard and the fringe lines that result from the reference mirror ofthe interferometer being tilted. In the depiction of FIG. 7 c, forillustrative simplicity, the calibration markings and fringe lines areshown according to a “split-screen” depiction. That is, the appearanceof the calibration standard markings 710 a through 710 f are shown onthe left hand side 702 of the optical image representation 701; and, theappearance of the fringe lines 711 a through 711 e are shown on theright hand side 703 of the optical image representation.

Note that, in the exemplary depiction of FIG. 7 c, the calibrationstandard should be placed upon the sample stage such that thecalibration markings run along the x axis. FIG. 8 shows a technique foraligning the fringe lines 711 a through 711 e to the calibrationmarkings 710 a through 710 e within the optical image that wasrepresented in FIG. 7 c. According to the methodology of FIG. 8, andreferring to FIGS. 4 b and 8 (noting that one should envision the sample460 of FIG. 4 b as being replaced by a calibration standard), the tiltangle of the reference mirror 404 is adjusted to set the spacing offringe lines 810 a through 810 e equidistant with the spacing of thecalibration markings 811 a through 811 e as observed in depiction 801 a.Here, recall from the discussion of FIG. 3 that the separation of thefringe lines are inversely proportional to the tilt angle θ of thereference mirror.

As fringe spacing is a function of the tilt angle θ, the fringe linespacing can be made to be equidistant with the calibration markingspacings by adjusting 820 the tilt angle θ as appropriate. Depiction 801a shows an embodiment where neighboring fringe line spacings are madeequidistant with neighboring calibration marking spacings. As such,neighboring calibration markings 810 a through 810 e having the samespacing (“Y”) as neighboring fringe lines 811 a through 811 e. In otherembodiments (e.g., where the density of fringe lines is greater than thedensity of calibration markings), a fixed number of fringe lines may beset per calibration marking. For example, as just one embodiment, 10fringe lines may be established per calibration marking allowing for afringe line density that is 10 times that of the calibration markingdensity of the calibration standard.

Note, however, that even though the depiction 801 a of FIG. 8 shows thefringe line spacings being equidistant with the calibration markingspacings, the fringe lines themselves 811 a through 811 e are notaligned with the calibration markings 810 a through 810 e. Here, theposition of the reference mirror 404 along the y axis may be adjusted821. That is, fringe lines can be made to move up or down along the zaxis of the detector by adjusting the y axis position of the referencemirror 404; and, according to the approach of FIG. 8, the y axislocation of the reference mirror 404 may be adjusted so that, asobserved in depiction 801 b, the fringe lines 811 a through 811 e “lineup with” the calibration markings 810 a through 810 e. Note that thefringe lines 811 a through 811 e are shown to be spaced apart a distanceof Y in depiction 801 b. This, again, traces back to the spacing of Ybetween neighboring markings of the calibration standard as originallyshown in FIG. 7 c. Note that the second process 821 is optional as thesetting of the fringe line spacings from process 820 establishesmeasurement accuracy in the xy plane of the sample stage.

Here, in conjunction with the mapping of the fringe lines to traces thatrun along the x axis of the sample stage 403 at specific y axislocations (as discussed in detail previously with respect to FIG. 4 a),the alignment of the fringe lines to a calibration standard that isplaced upon the sample stage 403 allows the relative spacing between thefringe lines to be precisely and accurately correlated to a specificdistance along the y axis of the sample stage 403. Thus, if a 1:1 fringeline to calibration marking ratio is established (and the calibrationmarkings are known to be spaced a distance of Y apart), the fringe linescan be used to measure surface changes of a sample as they occurprecisely Y apart along the y axis of the sample stage. Similarly, asanother example, if a 10:1 fringe line to calibration marking ratio isestablished (and the calibration markings are known to be spaced adistance of Y apart), the fringe lines can be used to measure surfacechanges of a sample as they occur precisely 0.1Y apart along the y axisof the sample stage.

In an embodiment, the understood distance between neighboring fringelines as they map to the xy plane of the sample stage is normalized bythe number of pixels between neighboring fringe lines as observed on thedetector. This calculation effectively corresponds to a distance alongthe y axis of the sample stage (and along the x axis of the samplestage) that each pixel corresponds to (i.e., a distance “per pixel”along both the x axis and the y axis of the detector that each pixelrepresents).

For example, if 10 pixels exist between neighboring fringe lines on thedetector; and, if neighboring fringe lines are understood to map tosample stage traces that are spaced a distance of Y apart as a result ofthe calibration process—then, a per pixel resolution of 0.1Y in both thex and y directions may be said to exist. In this case, for example, astring of 5 consecutive pixels along the x axis of the detector can berecognized as mapping to a distance of 0.5Y over the surface of thesample stage (or sample); and, likewise, a string of 5 consecutivepixels along the z axis of the detector can be recognized as mapping toa distance of 0.5Y over the surface of the sample stage (or sample).

Here, recalling that a pre-established measurement scale can bepartially formed by recording information related to the mapping of thedetector's fringe lines to the sample stage, note that storing this perpixel resolution in the x and y direction qualifies as storinginformation that can be used toward this objective. For example, if theper pixel resolution in the x and y direction corresponds to a distanceof 0.1Y; then, undisturbed fringe lines detected to be 30 pixels apartalong the z axis of the detector can be recognized as representingtraces spaced a distance of 3Y apart along the y axis of the samplestage. Similarly, if fringe lines extend 100 pixels across the x axis ofthe detector; then, these same fringe lines may be recognized as tracesthat run over a distance of 10Y along the x axis of the sample.

Lastly, note that distinction should be drawn between the previouslydiscussed “per pixel unit of sample height measurement” (and, which isdiscussed in more detail immediately below) and the just discussed “perpixel” distance along the x and y axis of the sample stage. Better said,according to the present measurement technique, pixel locations can beused not only to identify a specific position in the xy plane of thesample stage but also to identify sample height along the z axis abovethe sample stage. The “per pixel” distance along the x and y axis of thesample stage is devoted to the former; while, the “per pixel unit ofsample height measurement” is devoted to the later.

3.2 Calculation of Per Pixel Unit of Sample Height Measurement

Referring back to FIG. 6, with the fringe lines being aligned 610 to acalibration standard (e.g., and perhaps a “per pixel” resolution in thex and y directions being recorded), the next procedure in establishing ameasurement scale is calculating 611 the per pixel unit of sample heightmeasurement. Recall from the discussion of FIG. 6 that the “per pixelunit of sample height measurement” represents the amount of unitdistance along the z axis above the sample stage that a fringe linedisturbance of one pixel along the z axis of the detector translates to.As interferometry is based upon optical path length differences betweenlight directed to the reference mirror and light directed to the samplestage, the introduction of a sample to the sample stage effectivelychanges the optical path length differences that existed prior to itsintroduction. Better said, at least a portion of the light that isdirected to the sample stage (rather than the tilted reference mirror)will have its optical path length shortened because it will reflect offof the sample rather than the sample stage.

This shortened optical path length corresponds to change in optical pathlength difference; which, in turn, causes a disturbance to the positionof a fringe line. Thus, in order to calculate the per pixel unit ofsample height measurement, the amount of disturbance in the positioningof a fringe line should be correlated to the change in optical pathlength that occurs when a sample is placed on the sample stage. Here, inorder to better comprehend the change in optical path length, ananalysis of an interferometer without a sample is in order; and, ananalysis of an interferometer with a sample is in order. FIGS. 4 a and 9a relate to the optics of an interferometer without a sample; and, FIG.9 b relates to the optics of an interferometer with a sample. Adiscussion of each of these immediately follows. By way of comparing theoptical conditions that exist with and without a sample (with particularfocus on the change in optical path length), the per pixel unit ofsample height measurement will be deduced.

Referring now to FIG. 4 a, assume a first distance 493 represents adistance of A between the θ=0° reference plane 499 and the tiltedreference mirror 404; and, a second distance 494 represents a distanceof 3λ/2 between the θ=0° reference plane 499 and the tilted referencemirror 404. It can be shown that, when a sample is not placed on thesample stage, a fringe line appears for every integer spacing of λ/2between the tilted reference mirror 404 and the θ=0° reference plane499. Thus, for example, a first fringe line 495 appears on the detector405 as a result of the first distance 493; and, a second fringe line 496appears on the detector 405 as a result of the second distance 494.

This property can be viewed “as if” there is a relationship between: 1)the “intercepts” on the tilted reference mirror 404 of each integerspacing of λ/2 between the tilted reference mirror 404 and the θ=0°reference plane 499; and, 2) the location of the fringe lines on thedetector itself 405. Better said, recalling from the discussion of FIG.3 that fringe lines 495, 496 are separated from one another according to˜λ/θ, note also that the intercepts 497, 498 of distances 493, 494 withthe tilted reference mirror 404 are spaced λ/(2 sinθ) apart along theplane of the tilted reference mirror 404 (because distance 494 is λ/2longer than distance 493; and, from basic geometry, the hypothenous of aright triangle is a leg of the triangle (λ/2) divided by the sin of theangle opposite the leg (sinθ)).

Here, as ˜λ/θ is consistent with λ/(2 sinθ) (particularly for a smallangle of θ), a correlated relationship can therefore be envisionedbetween the: 1) the spacing between the intercepts upon the tiltedreference mirror 404 of each integer λ/2 spacing between the tiltedreference mirror 404 and the θ=0° reference plane 499; and, 2) thespacing between the fringe lines that appear on the detector 405.

FIGS. 9 a and 9 b show an example of the change in fringe line positionthat occurs when a sample is placed on a sample stage. In particular,FIG. 9 a provides further optical analysis when a sample is not placedon the sample stage; and, FIG. 9 b provides an optical analysis when asample is placed on the sample stage. By comparing the pair of analysis,a suitable understanding of the per pixel unit of sample heightmeasurement can be formulated.

Like FIG. 4 a, FIG. 9 a shows an interferometer 910 without a sample onits sample stage 903 a. When an interferometer does not have a sample onits sample stage 903 a, the variation in optical path length differencebetween light directed to the sample stage 903 a and light directed tothe tilted reference mirror 904 a (that causes the appearance of fringelines on the detector 905 a) is largely a function of the distancebetween the θ=0° reference plane 999 a and the tilted reference mirror904 a. Here, when a sample is not placed on the sample stage 903 a, alllight directed to the sample stage 903 a travels the same distance d1 intraveling from the splitter 902 a to the sample stage 903 a (and backagain).

Thus, the “variation” in path length from the splitter 902 a to thetilted reference mirror 904 a can be viewed as the “primary contributor”to the “variation” in optical path length difference that occurs betweenlight directed to the sample stage 903 a and light directed to thetilted reference mirror 904 a; which, in turn, causes the appearance ofmultiple fringe lines on the detector 905 a. Here, as the “variation” inpath length from the splitter 902 a to the tilted reference mirror 904 aclearly occurs within the region between the θ=0° reference plane 999 aand the tilted reference mirror 904 a, the region between the θ=0°reference plane 999 a and the tilted reference mirror 904 a serves as aprimary region on which to focus the optical analysis.

Recall that, without a sample being placed on the sample stage 903 a, afringe line appears for every integer spacing of λ/2 between the tiltedreference mirror 904 a and the θ=0° reference plane 999 a; and that, acorrelating relationship can be envisioned between the spacing of thefringe lines on the detector and the intercept spacings on the tiltedreference mirror 404. As such, FIG. 9 a shows a first fringe line 995 aacross a portion of a CCD detector 905 a that results from a spacing 993a of A between the θ=0° reference plane 999 a and the tilted referencemirror 904 a; and, a second fringe line 996 a across the same portion ofa CCD detector 905 a that results from a spacing 994 a of 3λ/2 betweenthe θ=0° reference plane 999 a and the tilted reference mirror 904 a.

Referring to FIG. 9 b, note that a sample 912 has been placed on thesample stage 903 b of the interferometer 911. Here, it is assumed thatthe sample 912: 1) has a height (as measured along the z axis) of λ/4;and, 2) is positioned at a y axis location on the sample stage 903 bthat mapped to fringe line 995 a prior to introduction of the sample 912(as observed in FIG. 9 a). In this case, the proper optical analysis canbe performed by superimposing the shape of the sample 912 over the θ=0°reference plane 999 b at the location of spacing 993 a that existedprior to the introduction of the sample 912.

FIG. 9 b shows this superposition, which, in turn, modifies the shape ofthe reference plane 999 b. Here, superimposing the shape of the sampleat the location of spacing 993 a reflects the fact that: 1) the sample912 is positioned at a y axis location on the sample stage 903 b thatmapped to fringe line 995 a (because spacing 993 a “caused” theappearance of fringe line 995 a); and, 2) a change in optical pathlength of λ/4 is caused to that portion of light that is now reflectingoff of the sample (rather than off of the sample stage).

The change in optical path length causes a disturbance to the positionof the fringe line 995 a because the optical path length difference (asbetween light directed to the sample stage and light directed to thereference mirror) has been changed by the introduction of the sample. Assuch, fringe line 995 a moves down along the detector 905 b to a newposition (as observed in FIG. 9 b by fringe line 995 b). The newposition for the fringe line 995 b corresponds to the same length ofspacing 993 b (i.e., A) between the reference plane 999 b and the tiltedreference mirror 904 b that existed before introduction of the sample.However, the modification to the shape of the reference place caused bythe shape of the sample 912 effectively brings the same length spacing993 b to a lower position along the z axis. As such, the fringe line 995b also moves down to a lower position on the surface of the detector 905b.

Here, a change of λ/4 drops the fringe line 995 b halfway between itsoriginal position 907 (before introduction of the sample 912) and fringeline 996 b. This arises naturally when one considers that spacing 993 bcan be broken down into a first segment that is 3λ/4 in length and asecond segment that is λ/4 in length (noting that a total length of λfor spacing 993 b is preserved). The λ/4 segment helps form a righttriangle (observed in FIG. 9 b) with the tilted reference mirror 904 b;which, from basic geometry, indicates that the intercept of spacing 993b with the tilted reference mirror 904 b will move λ/(4 sinθ) along theplane of the reference mirror 904 b as a consequence of the sample 912being introduced to the interferometer 911. Since, there is correlatingrelationship between the location of the “intercept” on the tiltedreference mirror 904 b and the location of the fringe line 995 b on thedetector itself 905 b, this corresponds to the movement of the fringeline 995 b consuming one half of the distance that once separated itfrom fringe line 996 b.

Consistent with the analysis provided just above, note that a sample 912height of λ/2 would have caused fringe line 995 b to drop far enough soas to completely overlap fringe line 996 b. As such, it is apparent thatthe “per pixel unit of sample height measurement” can be calculated asλ/(2N) where N is the number of pixels between neighboring fringe lineson the CCD detector 905 a when a sample is not placed on the samplestage 904 a (as observed in FIG. 9 a). For example, referring to FIG. 9a, note that there are 10 pixels between neighboring fringe lines 995 aand 996 a. For a light source having a wavelength of λ=20 nm, thiscorresponds to a “per pixel unit of sample height measurement” of 1 nmper pixel (i.e., 20 nm/20 pixel=1 nm/pixel). As such, because theintroduction of the sample caused fringe line 556 a,b to move fivepixels, in this example, the sample height can be precisely calculatedas 5 nm.

Referring then back to FIG. 6, the “per pixel unit of sample heightmeasurement” can be calculated 611 from the wavelength of the lightsource λ; and, the number of pixels that are observed to exist betweenfringe lines when a sample is not placed onto the sample stage. Here,note that the process of aligning 610 the fringe lines with thecalibration standard may adjust the spacing between fringe lines on thedetector; and, as such, the calculation 611 of the “per pixel unit ofsample height measurement” should be made after the position of thefringe lines have been aligned 610.

In an embodiment, once the “per pixel unit of sample height measurement”is calculated 611, information related to the mapping of the detector'sfringe lines to the sample stage is stored 612 along with the “per pixelunit of sample height measurement”; which, as already discussed above,corresponds to the storage of information that can be used toeffectively construct a measurement scale against which fringe linechanges can be measured to determine the topography of a sample.

4.0 Embodiment of Apparatus

FIG. 10A shows an embodiment of a test measurement system that iscapable of determining a surface topography by comparing the fringelines that emerge when a sample is placed on the sample stage 1003against a pre-established measurement scale. The test measurement systemof FIG. 10A includes a light source 1001 and a splitter 1002. The lightsource may be implemented with different types of light sources such asa gas laser, a semiconductor laser, a tunable laser, etc. A collimatinglens or other device may be used to form planar wavefronts from thelight from the light source 1001. The splitter 1002 is oriented todirect a first portion of the light from the light source to a referencemirror 1004; and, a second portion of the light from the light sourcetoward a sample stage 1003. The splitter 1002 may be implemented with anumber of different optical pieces such as glass, pellicle, etc.

In order to properly direct light as described above, the splitter 1002is positioned at an angle α with respect to a plane where a surfacetopology measurement is made (e.g., the xy plane as seen in FIG. 10A).In a further embodiment, α=45°; but those of ordinary skill will be ableto determine and implement a different angle as appropriate for theirparticular application. The splitter 1002 may also be designed to direct50% of the light from the light from the light source 1001 toward thereference mirror 1004 and another 50% of the light from the light fromthe light source 1001 toward the sample stage 1003. But, those ofordinary skill will be able to determine other workable percentages.

In a broader sense, the reference mirror 1004 may be viewed as anembodiment of a reflecting plane that reflects light back to thesplitter 1002. A reflecting plane may be implemented with a number ofdifferent elements such as any suitable reflective coating formed over aplanar surface. The reflecting plane may be tilted at an angle θ so thatsuitably spaced fringe lines appear along the surface of a detector1005. As discussed, the positioning of θ can be adjusted in order toalign the fringe lines to a calibration standard.

The sample stage 1003 supports the test sample whose surface topographyis to be measured. After light is reflected from the sample stage 1003and/or a sample placed on the sample stage 1003, it is combined withlight reflected from the reference mirror 1004. The combined light isthen directed to detector 1005. In a broader sense, the detector 1005may be viewed as an opto-electronic converter that converts the opticalintensity pattern at the detector surface into an electricrepresentation. For example, as discussed previously, the detector 1005can be implemented as a charge coupled device (CCD) array that isdivided into a plurality of pixels over the surface where light isreceived. Here, an output signal is provided for each pixel that isrepresentative of the intensity received at the pixel.

A fringe detection unit 1006 processes the data that is generated by thedetector 1005. The fringe detection unit 1006 is responsible fordetecting the position(s) of the various fringes that appear on thedetector 1005. An embodiment of a fringe detection unit 1006 isdescribed in more detail below with respect to FIGS. 11 a through 11 c;however, it is important to recognize that the fringe detection unit1006 can be implemented in vast number of ways. For example, the fringedetection unit 1006 may be implemented as a motherboard (having acentral processing unit (CPU)) within a computing system (such as apersonal computer (PC), workstation, etc.). Here, the detection offringes may be performed with a software program that is executed by themotherboard. In other embodiments, the fringe detection unit 1006 may beimplemented with dedicated hardware (e.g., one or more semiconductorchips) rather than a software program. In other embodiments, somecombination of dedicated hardware and software may be used to detect thefringes.

FIGS. 11 a through 11 c elaborate further on at least one embodiment ofthe fringe detection unit. FIG. 11 a provides a methodology 1100 forperforming fringe detection. FIG. 11 b provides an embodiment of adedicated hardware circuit 1150 that effectively performs themethodology of FIG. 11 a. FIG. 11 c displays waveforms that areapplicable to the circuit of FIG. 11 b. According to the methodology ofFIG. 11 a, fringes are detected by taking the first derivative 1104 of acolumn of detector array data. A column of detector array data is thecollection of optical intensity values from the pixels that run alongthe same column of a detector's pixel array. For example, if array 1101of FIG. 11 a is viewed as the CCD detector of an interferometer, a firstcolumn 1102 that traverses the array will encompass a “first” column ofCCD data, a second column 1103 that traverses the array will encompass a“second” column of CCD data, etc.

The optical intensity values from a column of CCD data should indicate aseries of relative minima. That is, as each column of CCD datacorresponds to a “string” of optical intensity values that impinge theCCD detector along the z axis and at the same x axis location, if theoptical intensity values are plotted with respect to their z axislocation, a collection of relative minimum points should appear. Thisfollows naturally when one refers, for example, back to FIG. 3 andrecognizes that by traveling along the optical intensity pattern 350 inthe +z direction at a fixed x coordinate a series of relative minimawill be revealed (e.g., at locations that correspond to fringe lines 352a, 352 b, 352 c). Another example is provided in FIG. 11 c where atypical distribution 1112 of optical intensity values along the z axisand at a fixed x location of the detector is presented.

From the depiction of FIG. 11 c, each relative minimum (e.g., at pointsz₂, z₄, z₆, z₈, etc.) will correspond to a fringe line (recalling that afringe line corresponds to a relative minimum optical intensity as aresult of destructive interference). As such, the pixel locations on thedetector where fringe lines appear can be precisely identified. Bettersaid, as the x coordinate of the column of CCD data being analyzed isknown (e.g., x_(n)); and, as the fringe detection process identifiesspecific z axis coordinates where a fringe line appears (e.g., z₂, z₄,z₆, z₈, etc.), a set of pixel coordinates (e.g., (x_(n),z₂); (x_(n),z₄);(x_(n),z₆); (x_(n),Z₈,);,etc.) that define the location of each instanceof a fringe line can be readily identified for each analysis of a columnCCD data.

Taking the first derivative 1104 of a column of CCD data (with respectto the z axis) and then determining 1105 where the first derivativechanges from a negative polarity to a positive polarity is a way toidentify the z coordinate for each pixel that receives a fringe line fora particular column of CCD data. Although such an approach could be donein software, hardware or a combination of the two, FIGS. 11 b and 11 crelate to an approach that uses dedicated hardware. Here, a column ofCCD data represented by waveform 1112 is provided to input 1108. Thecolumn of CCD data 1112 is then presented to both a comparator 1106 anda delay unit 1107. The delay unit effectively provides a delayed orshifted version of the column of CCD data 1112 (as observed withwaveform 1113).

The comparator 1109 indicates which of the pair of waveforms 1112, 1113is greater. Waveform 1114 provides an example of the comparator output1109 signal that is generated in response to waveforms 1112, 1113. Notethat a rising edge is triggered for each relative minima (e.g., atpoints z₂, z₄, z₆, z₈, etc.). One of ordinary skill will recognize thatindicating which of the pair of waveforms 1112, 1113 is greatermathematically corresponds to taking the first derivative 1105 ofwaveform 1112 and determining its polarity. Here, determining where thepolarity changes from negative to positive corresponds to identifying arelative minimum (because the slope of a waveform changes from negativeto positive at a relative minimum). As such, as seen in FIG. 11 c, eachrising edge of the comparator output signal should line up with eachrelative minima of the column of CCD data.

4.0 Embodiment of A Pre-Established Measurement Scale and A TopographyMeasurement Based Thereon

Referring back to FIG. 10A; and, with a description of an embodiment forthe fringe detection unit 1006 having been completed (as described justabove with respect to FIGS. 11 a through 11 c), the present sectiondiscusses at length an embodiment of the operation of the topographymeasurement unit 1007. The operation of the topography measurement unitis discussed by way of describing how a precise topography descriptioncan be developed. However, before commencing such a discussion, a briefreview of the overall methodology will be provided as well as a briefdigression into specific details concerning the establishment of themeasurement scale.

Referring back to FIG. 5, recall that a measurement scale is firstestablished 501 before a topography measurement is made 503. Here, FIGS.6 through 9 b helped illustrate that the measurement scale can bedeveloped by: 1) aligning the fringe lines to a calibration standardwithout a sample being placed on the sample stage; 2) recognizing themapping of the detector's fringe lines to the sample stage; and, 3)recognizing the per pixel unit of sample height measurement. Thus, in anembodiment, the storage of measurement scale information involves thestoring of the fringe line positions of an interferometeric image when asample has not been introduced to the interferometer. This effectivelyacts as a baseline against which the fringe line disturbances that occurin response to a sample being introduced to the interferometer arecompared.

From the discussion of fringe line detection (as performed by the fringedetection unit 1006) provided just above with respect to FIGS. 11 athrough 11 c, it is apparent that the location of the fringe lines overthe entirety of the detector 1005 can be determined by performing afringe detection analysis for each detector column. Thus, a measurementscale can be created by: 1) aligning the fringe lines to the calibrationstandard without a sample being introduced to the interferometer; 2)detecting the pixel locations where the fringe lines appear on thedetector (e.g., by performing fringe detection for each detectorcolumn); 3) storing these pixel locations; 4) storing or otherwiserecognizing the distance between tracings on the sample stage (asdetermined through the manner in which the fringe lines map to thesample stage—for example, with the help of a per pixel resolution in thex and y direction parameter)—or, by simply recording the calibrationstandard spacing; and 5) storing or otherwise recognizing the per pixelunit of sample height measurement based upon the fringe line separation.

FIG. 12 a represents the pixel location information which may be storedto help form a stored measurement scale. Here, an array of detectorpixel locations are observed and an “X” is placed in each location wherea fringe line is detected when a sample is not placed on the samplestage. Thus, as seen in the example of FIG. 12 a, five fringe lines1201, 1202, 1203, 1204 and 1205 are detected. The components ofinformation that can be stored so that a measurement scale can beutilized therefrom may therefore include: 1) the understood spacingbetween the tracings on the xy plane of the sample stage that the fringeline separations observed on the detector map to (and/or a parameterfrom which the spacing can be determined such as the per pixel change inx and y direction parameter discussed previously); 2) the location ofeach fringe line on the detector (e.g., the (x,z) pixel coordinate ofeach pixel having an “X” in FIG. 12); and 3) the “per pixel unit ofsample height measurement” as calculated once the tilt angle of thereference mirror is established. The relevance of each of these isdescribed immediately below.

Recall from FIG. 8 that the alignment of the fringe lines 811 a–811 e tothe calibration standard markings 810 a–810 e allow the fringe lines 811a–811 e to respectively map to sample stage tracings that are spaced adistance of “Y” apart along the y axis of the sample stage. FIG. 12 ademonstrates that the stored measurement scale recognizes the separationalong the y axis of the sample for each detected fringe line. Forexample, as just one approach, one fringe line (e.g., fringe line 1203)may be recognized as the “baseline” fringe having a corresponding (i.e.,“mapped to”) y axis location on the sampled stage defined at y=0.

In an embodiment where each fringe line maps to a trace that runs alongthe x axis of the sample and that is spaced Y apart from the trace of aneighboring fringe line on the sample stage, trace 1204 will correspondto a y axis location on the sample of y=−Y and trace 1202 willcorrespond to a y axis location on the sample of y=+Y. Similarly, trace1205 will correspond to a y axis location on the sample of y=−2Y andtrace 1201 will correspond to a y axis location on the sample of y=+2Y.Note that, briefly referring back to FIG. 4 a, “higher” fringe lines onthe z axis of the detector 405 will map to “lower” positions along the yaxis of the detector. As such, the fringe lines 1202, 1201 positionedbelow the baseline fringe 1203 are given a positive polarity; whilefringe lines 1204, 1205 positioned above the baseline fringe 1203 aregiven a negative polarity.

Keeping track of the location of each fringe line on the detector (e.g.,the (x,z) pixel coordinate of each pixel having an “X” in FIG. 12 a),effectively corresponds to the location of a number of different “sub”measurement scales that are located at a specific y axis locations alongthe sample stage surface. FIG. 12 b shows a drawing of this perspectivewhere a collection of measurement scales that each measure sample heightalong the x axis at a unique y axis location are observed. That is,another way of looking at the pre-established measurement scale, forembodiments where fringe line spacings map to a distance of Y upon thesample stage, is a translation of information received on the detectorto a plurality of measurement scales that: 1) are spaced apart adistance Y along the y axis of the sample stage; 2) stand “upright” onthe sample stage so as to measure sample height above the sample stage(via the “per pixel unit of measurement height” parameter); and 3) runalong the x axis of the detector.

Note that keeping track of the fringe detection locations corresponds toa degree of data compression because pixel coordinates that are notassociated with a fringe line (i.e., those not having an “X” in FIG. 12)can be disposed of. Furthermore, as a case of further data compression,if all the fringe detections for a particular fringe line (e.g., each“X” associated with fringe line 1205) lay along the same z axiscoordinate—only one data value needs to be stored to represent theentire fringe line (i.e., the z axis coordinate). In order to properlyrecord measurement scale information, the per pixel unit of sampleheight measurement is also recorded. Note that if “bending” appears inthe fringe lines (e.g., due to imperfect optics) correction factors maybe applied on a pixel by pixel basis to the fringe line data in order to“straighten out” a fringe line.

As described above with respect to FIGS. 9 a and 9 b; and, as describedimmediately below, the per pixel unit of sample height measurement isused to help define the height of the sample at a particular location byfactoring it with the disturbance (in pixels) that occurs at aparticular (x,z) coordinate location in response to a sample beingplaced on the sample stage. In a sense, each pixel on the detectorcorresponds to a “tick” along the vertical axis (i.e., along the z axis)of any of the measurement scales observed in FIG. 12 b; where, thedistance between “ticks” is the per pixel unit of sample height.

FIG. 13 shows a representation of the fringe lines of FIG. 12 a afterthey have been disturbed in response to the placement of a sample on thesample stage. Here, fringe line 1301 of FIG. 13 corresponds to fringeline 1201 of FIG. 12 a, fringe line 1302 of FIG. 13 corresponds tofringe line 1202 a of FIG. 12, etc. Note that the fringe lines 1301–1305of FIG. 13 also correspond to the fringe lines 451 e through 451 a ofFIG. 4 b that trace out the profile of a sample 460 having a trapezoidalshape. FIG. 14 shows the result when the differences betweencorresponding fringe lines from FIGS. 13 and 12 a (i.e., the fringe linedisturbances) are calculated. For example, by subtracting the fringelines of FIG. 12 a from their corresponding fringe lines of FIG. 13(i.e., subtracting fringe line 1205 from fringe line 1305, subtractingfringe line 1204 from fringe line 1304, etc.) and multiplying by −1 (tocorrect for the inverted topography profiles observed in FIG. 13) theprofiles 1401 through 1405 of FIG. 14 will result.

Each profile 1401 through 1405 corresponds to an accurate description ofthe sample's topography at the y axis locations that are defined by themeasurement scale. Note that topography profiles 1401 through 1405 aremeasured vertically in terms of pixels; and, as a result, the “per pixelunit of sample height measurement” parameter can be used to preciselydefine the sample's height at each x axis location. For example, notethat the trapezoid profile reaches a maximum height of 3 pixels. Here,if the “per pixel unit of sample height measurement” parametercorresponds to 1 nm per pixel, the sample will have a measured maximumheight of 3 nm.

While FIGS. 12 a, 13 and 14 helped to describe an embodiment of theoperation of the topography measurement unit 1007 of FIG. 10A, FIG. 15shows an embodiment 1507 of a circuit design for the topographymeasurement unit 1007 observed in FIG. 10A. According to the design ofFIG. 15, the stored measured scale data and disturbed fringe line dataare received at inputs 1522 and 1521, respectively. Here, informationassociated with FIG. 12 a may be regarded as some of the storedmeasurement scale data (excluding the per pixel unit of sample of heightand the sample stage y axis location that each undisturbed fringe linecorresponds to); and, the fringe line patterns observed in FIG. 13 maybe regarded as an example of disturbed fringe line data responsive to asample being placed on the sample stage. In this case, note that input1521 of FIG. 15 corresponds to input 1021 of FIG. 10A; and, input 1522of FIG. 15 corresponds to input 1022 of FIG. 10A. Note that, in theparticular embodiment of FIG. 10A, the sample data and the storedmeasurement scale data are extracted from their own memory regions 1024,1023. If a common memory is used, inputs 1021, 1022 may merge to acommon data path.

The fringe line extraction unit 1501 extracts corresponding fringe linesfor comparison from their appropriate memory regions 1523, 1524. Here,corresponding pairs of fringe lines may be extracted in light of themanner in which they were stored. For example, if the z axis pixelcoordinates for a first fringe line associated with the measurementscale information (e.g., fringe line 1201 of FIG. 12) may beautomatically stored (by the detection unit 1006) in a first region ofmemory 1524; and, if the z axis pixel coordinates for a first disturbedfringe line associated with sample information (e.g., fringe line 1301of FIG. 13) is automatically stored in a first region of memory 1523 (bythe detection unit 1006), these same sets of fringe line data may beextracted by the fringe line extraction unit 1501 by automaticallyreferring to these same memory regions. Thus, fringe lines 1201 and 1301may be presented together at inputs 1522, 1521, respectively; fringelines 1202 and 1302 may be presented together at inputs 1522, 1521,respectively;, etc.

The sample stage y axis location for these fringe lines may be kepttrack of (e.g., by being stored along with the pixel locations of eachundisturbed fringe line in memory 1524) so that the analysis of the pairof fringe lines that are together presented at inputs 1522, 1521 can betraced to a specific sample stage y axis location. Once a pair ofcorresponding fringe lines have been extracted, the differences betweenthe disturbed and disturbed locations are calculated and then multipliedby −1 to properly invert the data (note that the factor of −1 may beremoved if the reference mirror tilt angle is pivoted at the bottom ofthe reference mirror rather than the top (as observed throughout thepresent description)).

This creates a new string of data that represents the sample profile (asmeasured in pixels) at the y axis location of the sample stage that thepairs of fringe lines correspond to (e.g., profile 1402 of FIG. 14). Assuch, multiplication of the pixel count at each x axis coordinate by the“per pixel unit of sample height measurement” parameter should producethe correct sample profile from the pair of fringe lines. Beyond thetopography measurement unit, the topography profiles may be stored ordisplayed. They may also be compressed through various data compressiontechniques to reduce the amount of data to be handled.

Referring back to FIG. 10A, it is important to recognize that thetopography measurement unit 1007 can be implemented in a vast number ofways and according to a vast number of different processing schemes. Forexample, the entire unit 1007 may be implemented with a motherboard(having a central processing unit (CPU)) within a computing system (suchas a personal computer (PC), workstation, etc.). Here, the developmentof topography profiles may be performed with a software program that isexecuted by the motherboard. Note that if the function of both thefringe line detection unit 1006 and the topography measurement unit 1007are implemented in software, a computing system may be employed afterthe O/E converter 1005 to perform the complete topography measurementanalysis.

As such, whether or not (or to what degree) data processing is performedthrough the execution of a software routine and/or dedicated hardware,the processing that is performed “behind” the detector may be viewed,more generically, as being performed by a “data processing unit” 1020.Here, the data processing 1020 unit may be implemented as dedicatedhardware (e.g., as suggested by FIG. 10A); or, alternatively or incombination, may be implemented with a computing system. An embodimentof a computing system is shown in FIG. 10B. General purpose processors,digital signal processors (DSPs) and/or general purpose/digital signalhybrid processors may be employed as appropriate as well.

Thus, any of the signal processing techniques described herein may bestored upon a machine readable medium in the form of executableinstructions. As such, it is also to be understood that embodiments ofthis invention may be used as or to support a software program executedupon some form of processing core (such as the Central Processing Unit(CPU) of a computer) or otherwise implemented or realized upon or withina machine readable medium. A machine readable medium includes anymechanism for storing or transmitting information in a form readable bya machine (e.g., a computer). For example, a machine readable mediumincludes read only memory (ROM); random access memory (RAM); magneticdisk storage media; optical storage media; flash memory devices;electrical, optical, acoustical or other form of propagated signals(e.g., carrier waves, infrared signals, digital signals, etc.); etc.

FIG. 10B shows an embodiment of a computing system 1000 that can executeinstructions residing on a machine readable medium (noting that other(e.g., more elaborate) computing system embodiments are possible. In oneembodiment, the machine readable medium may be a fixed medium such as ahard disk drive 1002. In other embodiments, the machine readable mediummay be movable such as a CD ROM 1003, a compact disc, a magnetic tape,etc. The instructions (or portions thereof) that are stored on themachine readable medium are loaded into memory (e.g., a Random AccessMemory (RAM)) 1005; and, the processing core 1006 then executes theinstructions. The instructions may also be received through a networkinterface 1007 prior to their being loaded into memory 1005.

In other embodiments, the topography measurement unit 1006 may beimplemented with dedicated hardware (e.g., one or more semiconductorchips) rather than a software program. In other embodiments, somecombination of dedicated hardware and software may be used to developthe topography profiles. Further still, multiple topography profiles maybe analyzed in parallel (e.g., with multiple implementations of thecircuitry of FIG. 15 that simultaneously operate on different sets offringe line pairs).

5.0 High Resolution Topographical Description Through Interleaving ofMultiple Topographical Measurements

FIGS. 16 a, 16 b and 17 relate to a technique for enhancing the overallresolution of the topography measurement along the y axis of the samplestage. Referring back to FIG. 10A, note that a stepper motor is coupledto the sample stage 1003 which can move the stage along the y axis.Here, for a trace separation of Y as discussed at length above, thesample stage can be moved a distance (e.g., less than Y) to effectivelyenhance the trace separation resolution.

For example, if the sample stage were moved along the y axis by anamount Y/2, the tracings of the fringe lines would effectively “move” soas to trace over new locations of the sample. FIG. 16 b demonstrates anexample of these new tracings. Note that these tracings may be comparedto the tracings originally observed in FIG. 4 b so as to compare themanner in which they have moved. FIG. 16 a provides the “new” samplefringes that are detected in response.

FIG. 17 provides an embodiment of the more thorough topographydescription that results when the topography information from FIGS. 13and 16 a are combined by aligning or otherwise interleaving theirprofiles at the appropriate y axis locations. The more thoroughtopography information may be subsequently stored into volatile memory(e.g., a semiconductor memory chip) or non-volatile memory (e.g., a harddisk storage device); and/or may be displayed on a screen so that thetopography information can be easily viewed. Note that the controlapplied to the stepper motor 1008 may be overseen by the data processingunit 1020 of FIG. 10A; and, as such, consistent with the descriptionprovided so far, such control may be managed by software, dedicatedhardware or a combination thereof.

It is important to note that other approaches can be used to effectivelyachieve the same or similar effect as described just above. That is,other optical techniques may be employed in order to effectively providecollections of tracings that can be interleaved together so as to form ahigher resolution image of the overall sample. For example, according toone approach, the phase of the light emanating from the light source isadjusted in order to “adjust” the positioning of the fringe lines on thedetector. Here, the activity of altering the phase of the light willhave a similar effect to that of moving the sample stage as discussedabove with respect to FIGS. 16 a, 16 b and 17.

That is, a new relative positioning of the mapping of the fringe linestraces over the sample will arise; which, in turn, creates a “new” setof tracings that can be interleaved with other sets of tracings (formedat different sample stage and/or light phase positionings) so as to formhigh resolution topography images. According to another relatedapproach, the position of the tilted reference mirror is moved along theoptical path axis (e.g., along the y axis as depicted in FIG. 10A) to“adjust” the positioning of the fringe lines.

Again, a new relative positioning of the mapping of the fringe linestraces over the sample will arise; which, in turn, creates a “new” setof tracings that can be interleaved with other sets of tracings. Furtherstill, different light wavelengths may be employed (e.g., different“colors” of light may be used). Here, however, a separate measurementscale should be established for each wavelength of light that isemployed.

Regardless as to whether or not or which technique (or combination oftechniques) is used to create different sets of interleavable tracings,a word about magnification and the fringe lines is also in order. Withrespect to magnification, referring back to FIG. 10A, note that amagnifying lens 1010 is included. The “per pixel unit of sample heightmeasurement” parameter and the “per pixel unit of distance along the xand y directions of the sample stage” parameter can be enhanced byincorporating magnification into the interferometer. For example, ifwithout magnification there exist 10 pixels between neighboring fringelines (e.g., as observed in FIG. 9 a), providing 10× magnification willeffectively move neighboring fringe lines to be 100 pixels apart ratherthan 10 pixels apart. Because the fringe lines are still to be regardedas being separated by a distance of λ/2, the per pixel unit of sampleheight measurement may still be determined from λ/(2N). As such, atenfold increase in N corresponds to a tenfold increase in per change insample height.

With respect to fringe lines, note also that (as discussed) the fringelines observed in FIG. 3 correspond to relative minima locationsobserved within the optical intensity pattern 350. More generally, asappropriate, fringe lines can be construed as any looked for intensityfeature within the optical intensity pattern (e.g., relative minimumpositions; relative maximum positions, etc.) whose position(s) is/aredisturbed in a manner as described in the preceding description as aconsequence of a sample being introduced to the sample stage. Lastly,note also that stepper motor 1009 can be used to adjust the position ofthe reference mirror 1004 along the y axis and/or adjust the tilt angleof the reference mirror.

6.0 Characterization of Sample Composition Through Analysis of FringeLine Intensity Information

FIGS. 18 a through 18 b relate to an ensuing discussion that describeshow the material composition of a sample can be determined throughanalysis of the intensity values of the fringe lines that are detectedfrom the interferometer detector. That, is recalling the discussion ofFIGS. 11 a through 11 c and 12 a, note that the detection of fringelines involves the identification of particular pixel locations. Assuch, once fringe lines have been successfully detected, the opticalintensity data used to determine the fringe lines may be disposed of.According a measurement technique described in the present section,however, the optical intensity information is regarded as usefulinformation from which further characterization of the sample, beyondsurface topography, may be developed.

More specifically, the material(s) from which the surface(s) of thesample are comprised may be determined by characterizing thereflectivity of the sample surface as a function of the opticalwavelength of the interferometer's lightsource. The solid linedgraphical component of FIG. 18 a provides an exemplary depiction of a“reflectivity vs. wavelength” curve. Here, as reflectivity vs.wavelength is a function of the micro-structural details of a reflectingsurface such as conductivity, lattice spacing, lattice type, etc.,; and,as particular materials or substances (e.g., a pure material such asCobalt (Co); or, an alloy or other combination of materials such asSilicon Nitride (Si₃N₄), “Nickel Iron” (Ni_(100-x)Fe_(x)), etc.) haveparticular values for these same micro-structural details, the“reflectivity vs. wavelength” curve of a particular material orsubstance often uniquely defines it.

Better said, different materials or substances tend to exhibit different“reflectivity vs. wavelength” curves; and, as such, by developing asample's “reflectivity vs. wavelength” curve, the material or substancefrom which it (the sample) is comprised can be determined. Here, ratherthan disposing the optical intensity values observed at the detector,they may be analyzed so as to determine a particular reflectivity of thesample for a particular wavelength of the interferometer's opticalsource.

By changing the optical source's wavelength; and, by monitoring thechange in reflectivity of the sample in response thereto, a“reflectivity vs. wavelength” curve can be measured for the sample.This, in turn, can be used to determine the material composition(s) ofthe sample itself. FIG. 18 a provides exemplary results from such ameasurement where specific measured reflectivity data points are plottedvs. the applied wavelength. As the data points trace out thereflectivity curve of the sample, the composition of the sample can bedetermined.

In various embodiments, optical intensities observed at the pixellocations where fringe lines are detected are used to perform thereflectivity analysis. Thus, in some cases, not only are the pixellocations of detected fringe lines employed (to develop the surfacetopography description of the sample); but also, the optical intensityvalues of the same fringe lines are used to help characterize thematerial(s) from which the sample is comprised.

However note also that, seizing upon the notion that a fringe line maybe construed where appropriate so as to correspond to something otherthan a relative minimum, it some cases it may useful to track relativemaximum optical intensity values rather than relative minimum opticalintensity values for the sake of performing a reflectivity analysis.Thus, in some cases, a fringe line used for topography purposes may bethe same fringe line used for reflectivity analysis (e.g., both arerelative minimum); while, in other cases a fringe line used fortopography purposes may be different from a fringe line used forreflectivity analysis (e.g., one is a relative minimum while another isa relative maximum).

Also, in further embodiments, interferometer characteristics that arespatially and/or wavelength dependent may be characterized beforehand sothat any resulting detrimental affect(s) upon a reflectivity measurementcan be successfully canceled out. For example, if a first pixel locationis known to observe less light intensity than a second pixel location(e.g., on account of optical imperfections associated with theinterferometer), those of ordinary skill will be able separate opticalintensity differences (as between the pair of pixels) that areattributed to the interferometer's imperfections from those that areattributable to the sample's own characteristic reflectivity properties.The same may be said for an interferometer's wavelength relatedinconsistencies or imperfections (if any).

In a simplest case, the methodology of which is observed in FIG. 18 b,the sample is assumed to be uniformly comprised of a single composition(e.g., the sample is uniformly comprised of Co; or, uniformly comprisedof Si₃N₄, etc.). Because of the uniform composition of the sample, thefringe lines are “free to move” over the surface of the detector withoutaffecting the overall reflectivity experiment. Here, recalling from theBackground that fringe lines are separated in accordance with ˜λ/θ, theadjusting 1811 of the optical source wavelength (λ) between reflectivitycalculations (or at least optical intensity recordings) 1810 will causethe fringe lines to move upon the surface of the detector. However,because spatial and wavelength related inconsistencies of theinterferometer can be canceled out; and because, the sample has uniformreflectivity, the “reflectivity vs. wavelength” curve can be recordedirrespective of fringe line position.

In a more likely scenario, which is elaborated upon in FIG. 18 c, it maybe more desirable to realign the fringe lines with each change inwavelength. That is, after the wavelength is changed 1821, an attempt ismade to re-position 1822 the fringe lines so that appear in the sameposition that they did during exposure at the previous wavelength. Thisallows the measurement to determine reflectivity at specific regions ofthe sample because of the manner in which they map to the sample stage.As such, should the sample be comprised of different mixtures ofmaterials or substances (e.g., a first regions is Silicon (Si) and asecond region is Copper (Cu)), the interferometer is capable ofidentifying different mixtures on a pixel-by-pixel basis.

That is, a first “reflectivity vs. wavelength” curve can be measured forthe portion of the sample that maps to a first pixel location; and, asecond “reflectivity vs. wavelength” curve can be measured for theportion of the sample that maps to a second pixel location. By keepingtrack of separate curves for different pixels (or perhaps differentgroups of pixels), should the sample have different materials/substancesat the mapped to locations, different “reflectivity vs. wavelength”curves will reveal themselves as between the different pixel locations.As such, different materials/substances can be identified at precisesample locations.

Fringe lines may be re-positioned 1822, for example, by adjusting thetilt angle of the reference mirror so as to compensate for the movementthat was caused by the change in wavelength. As such, a “new” data pointfor a “reflectivity vs. wavelength” curve can be generated by: 1)changing 1821 the wavelength of the lightsource; 2) adjusting 1822 thefringe lines so as to overlap with their position(s) that existed priorto the wavelength change; and 3) calculating and storing reflectivity atthe fringe lines (or at least storing the observed intensity so thatintensity can be later calculated) 1820. Note that reflectivitycalculations can be readily made by those of ordinary skill becausethose of ordinary skill recognize that observed intensity isproportional to the reflectivity of the sample.

Note that, similar to the technique discussed previously with respect toFIGS. 16 a, 16 b and 17, once a first group of reflectivity curves havebeen developed for a first set of fringe line positions (e.g., bylooping through the methodology of FIG. 18 c multiple times for thefirst set of fringe line positions), a second group of reflectivitycurves may be developed for a second set of fringe line positions (e.g.,by looping through the methodology of FIG. 18 c multiple times for thesecond set of fringe line positions).

The corresponding groups of reflectivity curves may then be interleaved(e.g., akin to the concept discussed with respect to FIG. 17) so thatsample composition can be determined to a finer degree of resolution.Note also that procedures for performing sample “reflectivity vs.wavelength” analysis (e.g., as described just above) may be combinedwith (e.g., by preceding or by following) procedures for determiningsample topography (e.g., as discussed in preceding sections) so that acomplete description of a sample that measures both its surfacetopography and its material composition can be realized.

Also, referring briefly back to FIG. 10 a, the data processing unit 1020may be configured to keep track of the measured reflectivity vs.wavelength curves (e.g., via software or hardware). Furthermore, thedata processing unit 1020 may be configured to compare the measuredcurves against a data-base of such curves for known materials orsubstances (e.g., by correlating the measured curves against the curvesstored in the database) so as to determine that a particular curvematches the curve of a known material or substance. Since many of thesetechniques can be implemented in software, they may be embodied in amachine readable medium.

7.0 Signal Processing Techniques For Measuring Fringe Line DisturbancesThat Extend Outside Their Associated Reference Fields

Referring back to FIG. 13, note that the fringe line disturbances are“agreeable” in the sense that each fringe line disturbance remainswithin its corresponding reference field. A reference field correspondsto the field of optical image data that resides adjacent to a fringeline that the fringe line, when disturbed, will first project into inorder to demonstrate a change in sample height. For example, referringto FIG. 12 a the field of image data between fringe lines 1204 andfringe line 1203 correspond to the reference field for fringe line 1204,the field of image data between fringe lines 1203 and fringe line 1202correspond to the reference field for fringe line 1203, etc.

Comparing FIGS. 12 a and 13 then, note that the combination of maximumsample height and fringe line spacing is such that each fringe linedisturbance is kept within its own reference field. This makes forrelatively straightforward generation of the sample topography profilesobserved in FIG. 14. That is, the pixel locations of an entire fringeline and its associated disturbances can be readily stored, alone (i.e.,without being accompanied by the pixel locations of other fringe lines)to a particular memory location (e.g., that is partitioned for thefringe's lines reference field) and compared to is correspondingundisturbed fringe line position.

Thus, in general, according to various embodiments, a pre-definedmaximum, measurable/allowable sample height may be recognized such thatfringe line disturbances are designed to be kept within theircorresponding field of reference. This keeps the signal processingneeded for deriving topographical information nearer a minimum degree ofsophistication. Note that any such “maximum height” configuration can beeasily established through manipulation of fringe line spacing (e.g.,adjustment of tilt angle θ). Furthermore, measurement resolution is notlost because interleaving techniques (e.g., as discussed with respect toFIGS. 16 a, 16 b and 17) can be used as appropriate to developtopographical descriptions having a desired resolution.

By contrast, however, should it be desirable to readily measure fringeline disturbances that breach their respective reference fields, morerobust signal processing techniques may be used to accurately “track” aparticular fringe line. That is, for example, if memory resources areagain partitioned so as to organize the storing of data according to theimage's reference fields, the pixel locations of different fringe linesmay reside within a common reference field. FIG. 19 a shows an exemplarydepiction of a fringe lines 1951 b, 1951 c, 1951 d observed on adetector 1905 that breach their corresponding reference fields.Correspondingly, note that segments BC, EF of fringe line 1951 b andsegments HI, JK of fringe line 1951 c reside within the same field ofreference field (that is located between undisturbed fringe linelocations 1913 and 1912).

FIG. 19 b shows an exemplary depiction of a sample 1960 that could causethe fringe line disturbances observed in FIG. 19 a. Here, note thatfringe lines 1951 a, 1951 b, 1951 c, 1951 d, 1951 e of FIG. 19 arespectively map to tracings 1952 a, 1952 b, 1952 c, 1952 d, 1951 e ofFIG. 19 b. Comparing sample 1960 of FIG. 19 b to sample 460 of FIG. 4 b,note that the taller sample 1960 of FIG. 19 b (as compared to theshorter sample 460 of FIG. 4 b) may have caused fringe lines 1951 b,1951 c, 1951 d to breach their respective reference fields.

7.1 Memory Partitioning on a Reference Field-by-Reference Field Basis

Before commencing a discussion of more sophisticated signal processingtechniques suitable for tracking multiple fringe lines within the samereference field, a brief discussion as to how memory resources used tostore the pixel data of detected fringe line disturbances (e.g., such asmemory 1023, 1523 of FIGS. 10 and 15, respectively) can be partitionedso as to store pixel data on a reference field by reference field basis.It is important to emphasize at the onset of this discussion that memorypartitioning on a reference field by reference basis can be undertakenregardless if fringe lines “are” or “are not” expected to breach theirrespective reference fields. As such, memory partitioning can be appliedto the signal processing techniques previously discussed with respect toFIGS. 13 through 15 as well as those environments where the fringe linesbreach their respective reference fields as observed in FIG. 19 a.

Analyzing stored image data on a reference field by reference fieldbasis allows for easy/efficient memory management. That is, the memoryresources used to store the disturbed image data (e.g., memory resource1023 of FIG. 10 a) can be viewed as being partitioned into the referencefield sections themselves. This, in turn, allows for easy memoryorganization/usage regardless of where fringe lines are detected on thedetector from measurement to measurement and sample to sample.

For example, according to one embodiment, the storage of the referencescale information includes the storage (e.g., into memory resource 1024of FIG. 10 a) of each z axis location on the detector where anundisturbed fringe line resides. As such, a first pre-established memorylocation can be reserved for the storage of the z axis location (e.g.,“z₁”) for a first undisturbed fringe line (e.g., fringe line 1205 ofFIG. 12 a), a second pre-established memory or register region can bereserved for the storage of the z axis location (e.g., “z₂”) for asecond undisturbed fringe line (e.g., fringe line 1204 of FIG. 12 a),etc.

As such, the borders of the reference fields (i.e., the locations ofneighboring, undisturbed fringe lines) are always stored in previouslydefined memory/register locations—regardless if the borders themselveschange from reference scale to reference scale. That is, for example,the first reference field can always be recognized as being bounded bythe z axis values z₁ and z₂ that have been stored between the first andsecond pre-established memory locations of memory 1024—even if the testequipment stores different measurement scale embodiments (e.g.,different fringe line spacings) over the course of its useful life.

As a consequence, the pixel locations of the detected fringe linedisturbances can be easily “binned” according to their particularreference field. Better said, with knowledge of the reference fieldborders, the fringe detection unit 1006 can store fringe line sectionswithin the same reference field region into a common region of memory1023 (e.g., referring to FIG. 19 a, the pixel coordinates of fringe linesections HI, BC, EF and JK can be stored into a common memory locationof memory 1023). Furthermore, these regions of memory 1023 can bepre-established as well (e.g., a first pre-established region of memory1023 is reserved for pixel values detected within a first referencefield—regardless of the z axis borders for the first reference field; asecond pre-established region of memory 1023 is reserved for pixelvalues detected within a second reference field—regardless of the z axisborders for the first reference field;, etc.).

Furthermore, the topography measurement unit 1007 can be configured toautomatically read from these pre-established regions of memory 1023 inorder to purposely extract data within a certain reference field andwithout knowledge of the specific z axis borders themselves. Forexample, the topography measurement unit 1007 may be pre-configuredto: 1) read from a first address (or group of addresses) to obtain thepixel locations of detected fringe lines within a “first” referencefield; 2) read from a second address (or group of addresses) to obtainthe pixel locations of detected fringe lines within a “second” referencefield;, etc, As such, access to the specific z axis border values arenot needed by the topography measurement unit according to thisperspective.

7.2 Tracking Multiple Fringe Lines within the Same Reference Field

As mentioned previously, memory resources may be partitioned on areference field by reference basis regardless as to whether or notfringe lines are expected to breach their corresponding referencefields. For example, referring to FIGS. 13 and 12 a: 1) the pixellocations of fringe lines 1205 and 1305 may be read from memories 1024,1023 as a consequence of reading the undisturbed and disturbed data fora first reference field (these may then be subtracted from one anotherto form topography profile 1405); 2) the pixel locations of fringe lines1204 and 1304 may be read from memories 1024, 1023 as a consequence ofreading the undisturbed and disturbed data for a second reference field(these may then be subtracted from one another to form topographyprofile 1404);, etc.

However, if fringe line disturbances are expected to breach theircorresponding reference fields, more sophisticated signal processingtechniques may be necessary. Better said, once fringe line disturbancesare allowed to breach their reference fields, different fringe lines mayoccupy the same reference space. As such, a technique should be usedwhere different fringe lines can be recognized within the same referencefield space so that their respective disturbance(s) can be correctlymeasured. For example, fringe line segment BC of FIG. 19 a represents agreater height above the sample stage that does fringe line segment HI.As such, the different fringe lines should be recognized so that theircorresponding, undisturbed positions can be used a reference formeasuring topography.

FIG. 20 shows a signal processing technique that emphasizes the trackingof the individual slopes (i.e., “edges”) of a fringe line disturbancesin order to deal with the presence of different fringe lines within acommon reference field. Furthermore, while a particular fringe linedisturbance edge is being tracked, calculations are made to translateeach fringe line disturbance position into its corresponding sampleheight (z_(s)). With knowledge of the specific locations in xy samplestage space, the signal processing technique is able to produce an“output” that corresponds to specific x, y, z_(s) data positions. Thesex,y z_(s) data positions can then be stored or plotted to display theoverall topography of the sample. Furthermore, as described in moredetail below, the technique allows for further compression of the pixeldata points to further reduce processing overhead.

According to the signal processing technique of FIG. 20, track edgesfrom different fringe lines are tracked 2001 across each reference fieldin a first direction (e.g., in a “downward” sloped direction as observedin FIG. 19 a). For example, in order to execute the first trackingsequence 2001, the technique may: 1) read from a memory the image datacorresponding to the reference field between undisturbed fringe linelocations 1914 and 1913; and, track the downward edge segment “AB” offringe line 1951 b; then, 2) read from a memory the image datacorresponding to the reference field between undisturbed fringe linelocations 1913 and 1912 and track the downward edge segments “BC” offringe line 1951 b and “Hi” of fringe line 1951 c;, etc. Eventually thereference field beneath undisturbed fringe line location 1911 will beprocessed signifying the end of sequence 2001.

Then, in over the course of executing the second tracking sequence 2001in an “upward” direction, the technique may (after the reference fieldsbeneath location 1911 and between locations 1911 and 1912 have alreadybeen processed): 1) read from a memory the image data corresponding tothe reference field between undisturbed fringe line locations 1913 and1912 and track the upward edge segments “EF” of fringe line 1951 b and“JK” of fringe line 1951 c; then, 2) read from a memory the image datacorresponding to the reference field between undisturbed fringe linelocations 1914 and 1913; and, track the upward edge segment “FG” offringe line 1951 b;, etc,. Eventually the reference field between fringeline locations 1915 and 1914 will be processed signifying the end ofsequence 2002.

FIGS. 21 a through 21 c are directed to an embodiment of a methodologythat may be used to process data in either the upward or downwarddirection. FIG. 21 a shows the methodology, FIG. 21 b relates to itsapplication in the “downward” direction, and, FIG. 21 c relates to itsapplication in the “upward” direction. An example of operation in eachdirection will be subsequently discussed. Referring to FIGS. 21 a and 21b, a reference field worth of data is read 2101 from its correspondingmemory location. Here, the reference field worth of data may beretrieved 2101 with an address location (or group of address locations)where the pixel locations for detected fringe lines that reside withinthe reference field in question are found within the memory.

Then, starting at its intercept with the upper border of the referencefield, each fringe line segment is “tracked” (e.g., by recognizing theexistence of proximate pixel locations) while translating it into sampleheight z_(s) at the proper xy sample stage positions 2102. The trackingand translating 2102 can be viewed as multidimensional 2102 ₁ through2012 _(n) where the dimension size depends on the number of differentfringe line segments that are to be processed. That is, if one segmentrequires processing in the downward direction (e.g., as is the case withrespect to the reference field between positions 1914 and 1913) n=1; iftwo segments require processing in the downward direction (e.g., as isthe case with respect to the reference field between positions 1913 and1912) n=2;, etc.

A fringe line segment may be tracked in the downward direction bystarting at its intercept with its “upper” border and searching for orotherwise recognizing the existence of (within the reference field data)a proximately located pixel coordinate (e.g., by scanning the data andseizing the closest pixel location that is “down and/or to the right” ofthe intercept—in simple cases this should correspond to just selectingthe pixel location having the next highest x value). The process is thencontinually repeated until the intercept point with the next lowerreference field is reached; or, the fringe line doubles back andrecrosses the upper border.

Each pixel location of a fringe line segment may be translated into itsappropriate x, y, z_(s) sample topography information through the use ofthe stored measurement scale information and an understanding of theoverall geometry and optics. In an embodiment, consistent with theillustrations provided herein, for any fringe line pixel location(x,z): 1) the appropriate sample stage x coordinate value is determinedby factoring the x coordinate of the pixel by a “per pixel resolution inthe x and y direction” parameter (e.g., such as that discussed towardthe end of section 3.1); 2) the appropriate sample stage y coordinatevalue is determined by reference to the particular fringe line beingtracked (e.g., fringe line 1951 b is understood to be y axis location −Yon the sample stage) and, 3) the appropriate sample height z_(s) isdetermined according to the relationshipz _(s) =REF2+(R−dz)where: a) REF2 is a “baseline reference” that takes into account howmany reference fields the fringe line has already breached; b) R is the“sample height per reference field breach”; and c) dz is the differencebetween the pixel's z axis detector location and the location of thelower reference field border REF1 (i.e., z-REF1) factored by a per pixelunit of sample height parameter. A more thorough discussion of each ofthese follows below.

REF2 can be viewed as a variable that is kept track of for each fringeline. That is, in various embodiments, a separate REF2 variable ismaintained for each fringe line being tracked. Each time a fringe linebreaches another reference field, its corresponding REF2 variable isincremented by N(Δz) where N is the number of pixels (along the z axisof the detector) between neighboring fringe lines and Δz is the perpixel unit of sample height (e.g., as discussed in section 3.2). Assuch, when a fringe line is within its field of reference (such asfringe line 1951 b segment AB) the REF2 variable is 0 has not yetbreached its field of reference.

When a fringe line breaches its first field of reference and needs to betracked across a second field of reference (such as fringe line 1951 bsegment BC), the fringe line's REF2 variable will be incremented to avalue of N(Δz) for the translation process that occurs in the fringeline's second field of reference. Similarly, should the fringe linebreach into a third field of reference, the fringe line's REF2 variablewill be incremented to a value of 2N(Δz) for the translation processthat occurs in the third field of reference, etc. As such, the REF2variable for a fringe line converts each field of reference breach intoa corresponding sample height distance.

Whereas the REF2 variable represents the amount of sample height thathas been measured “so far” for a particular fringe line, R (the “sampleheight per reference field breach”) represents the field of sampleheight locations that are implicated by the tracking of the fringe linewithin the field of reference that is currently being processed. Assuch, R is a fixed value of N(Δz). Here, for any detector z axislocation, the term R-dz effectively represents, how far into the currentreference field the fringe line has extended. That is, as dz representsthe per pixel unit of sample height Δz factored by the distance aboveREF1 (referring to FIG. 21 b) that a particular pixel locationcorresponds to, when dz is 0, the fringe line has completed expanded thereference field so as to intercept the next lower field of reference(e.g., point B in FIGS. 21 b and 19 a); and, when dz is R/2 the fringeline has breached halfway into the current reference field, etc.

When the “downward” sloped fringe lines have been tracked in a referencefield, the looping nature of the methodology of FIG. 21 a indicates thatthe data for a next lower reference field will be extracted andanalyzed. For example, after the reference field between locations 1914and 1913 is analyzed (so as to track segment AB of fringe line 1951 b),the reference field between locations 1913 and 1912 will be analyzednext (so as to track segments BC of fringe line 1951 b and HI of fringeline 1951 c), etc. Here, in between a pair of reference field analysis',the intercept point of each fringe line is identified/recorded 2103 foreach fringe line that has breached into a next lower reference field(e.g., points C and I after the reference field between locations 1913and 1912 is analyzed).

For those fringe lines that do not breach into the next field ofreference some form of data compression may be undertaken. For example,in the case of fringe line 1951 b when the reference field betweenlocations 1912 and 1911 is being analyzed, the data tracking process maybe terminated at point D1 such that only the edges of the sample areactually measured. Alternatively, the tracking process may be sloweddown from point D1 to point D2 so that the density of translated samplepoints is reduced when running across a flat plane of the sample. Eitherof these techniques reduces the number of pixel locations used fortopography information; which, in turn, corresponds to a form of datacompression.

After the downward sloped fringe line edges are tracked, a similarprocess is repeated but in the opposite, upward direction. Here, themethodology of FIG. 21 a may again be referred to. FIG. 21 c relates tothe processing of the fringe line segment EF of fringe line 1951 b (whenthe reference field between locations 1913 and 1912 is analyzed). Here,the processing in the upward direction is similar to that of thedownward direction.

The most significant difference is that, in one embodiment, theappropriate sample height z_(s) is determined according to therelationshipz _(s) =REF2−dzwhere REF2 is the same “baseline reference” that takes into account howmany reference fields the fringe line has already breached—but, in theupward direction it is decremented (rather than incremented) by N(Δz)each time a higher reference field is analyzed. Note that the lowerborder for purposes of determining dz in this case is REF2. Once all thefringe lines have been tracked and the tracking process reaches thehighest field of reference, a collection of (x,y,z_(s)) data points areleft remaining that describe the topography of the sample in threedimensions. Those of ordinary skill will be able to develop topographymeasurement unit 1007 software and/or hardware that can perform thetechniques described just above.

8.0 Closing Statement

In the foregoing specification, the inventions have been described withreference to specific exemplary embodiments thereof. It will, however,be evident that various modifications and changes may be made theretowithout departing from the broader spirit and scope of the invention asset forth in the appended claims. The specification and drawings are,accordingly, to be regarded in an illustrative rather than a restrictivesense.

1. A method, comprising: a) measuring a first set of interferometerfringe line disturbances detected on a pixilated detector againstpre-determined measurement scale information in order to generate afirst set of profiles that describe the topography of a sample that isplaced upon a sample stage associated with said interferometer, saidpre-determined measurement scale information comprising a per-pixel unitof sample height that is used during said measuring to convert saidfirst set of disturbances into said first set of profiles said first setof profiles mapping to traces that run over a first axis of said sampleand said sample stage, said traces having a recognized spacing betweenone another along a second axis of said sample and said sample stage; b)adjusting the relative position of said traces to said sample so as tocreate a second set of fringe line disturbances; c) measuring saidsecond set of interferometer fringe line disturbances against saidpre-determined measurement scale information in order to generate asecond set of profiles that describe the topography of said sample; andd) interleaving said first set of profiles and said second set ofprofiles to create a topography description of said sample having aresolution along said second axis that is smaller than said spacing. 2.The method of claim 1 further comprising storing said topographydescription.
 3. The method of claim 2 wherein said storing furthercomprises storing into a volatile memory.
 4. The method of claim 2wherein said storing further comprises storing into a non-volatilememory.
 5. The method of claim 1 further comprising displaying saidtopography description on a screen so that said topography descriptioncan be viewed.
 6. The method of claim 1 wherein said measuring a firstset of interferometer fringe line disturbances further comprises: a)detecting said fringe line disturbances from an optical intensitypattern provided from a detector associated with said interferometer;and b) comparing the shapes of said detected fringe line disturbances attheir respective locations against said pre-determined measurement scaleinformation to form said first set of profiles, said pre-determinedmeasurement scale information further comprising the shapes of saiddetected fringe line disturbances at their respective positions whensaid fringe line disturbances were undisturbed.
 7. The method of claim 6wherein said detecting said fringe line disturbances further comprisesdetecting the relative minima within said optical intensity pattern. 8.The apparatus of claim 6 further comprising compressing the data fromwhich said first set of profiles are comprised.
 9. An apparatus,comprising: a) an interferometer, said interferometer furthercomprising: 1) a sample stage upon which a sample is placed and 2) apixilated detector that observes a plurality of fringe lines; and b) adata processing unit comprising a fringe detection unit and a topographymeasurement unit wherein: 1) said fringe detection unit is to measure afirst set of fringe line disturbances against pre-determined measurementscale information in order to generate a first set of profiles thatdescribe the topography of said sample, said pre-determined measurementscale information comprising a per-pixel unit of sample height that isused during said measuring to convert said first set of disturbancesinto said first set of profiles, said first set of profiles mapping totraces that run over a first axis of said sample and said sample stage,said traces having a recognized spacing between one another along asecond axis of said sample and said sample stage; 2) the relativeposition of said traces are adjusted relative to said sample so as tocreate a second set of fringe line disturbances; 3) said fringe linemeasurement unit is also to measure said second set of interferometerfringe line disturbances against said pre-determined measurement scaleinformation in order to generate a second set of profiles that describethe topography of said sample; d) said topography measurement unit is tointerleave said first set of profiles and said second set of profiles tocreate a topography description of said sample having a resolution alongsaid second axis that is smaller than said spacing.
 10. The apparatus ofclaim 9 wherein said data processing unit comprises memory to store saidtopography description.
 11. The apparatus of claim 10 wherein said dataprocessing unit is designed to store said topography description into avolatile memory.
 12. The apparatus of claim 10 wherein said dataprocessing unit is designed to store said topography description into anon-volatile memory.
 13. The method of claim 9 wherein said dataprocessing unit is designed to display said topography description on ascreen so that said topography description can be viewed.
 14. Theapparatus of claim 9 wherein said fringe detection unit measures a firstset of interferometer fringe line disturbances by: a) detecting saidfringe line disturbances from an optical intensity pattern provided froma detector associated with said interferometer; and b) comparing theshapes of said detected fringe line disturbances at their respectivelocations against said pre-determined measurement scale information toform said first set of profiles, said pre-determined measurement scaleinformation further comprising the shapes of said detected fringe linedisturbances lines at their respective positions when said fringe linedisturbances lines were undisturbed.
 15. The apparatus of claim 14wherein said fringe detection unit said detects said fringe linedisturbances by detecting the relative minima within said opticalintensity pattern.
 16. The apparatus of claim 14 wherein said dataprocessing unit compresses the data from which said first set ofprofiles are comprised.
 17. An apparatus, comprising: a) means formeasuring a first set of interferometer fringe line disturbancesdetected on a pixilated detector against pre-determined measurementscale information in order to generate a first set of profiles thatdescribe the topography of a sample that is placed upon a sample stageassociated with said interferometer, said pre-determined measurementscale information comprising a per-pixel unit of sample height that isused during said measuring to convert said first set of disturbancesinto said first set of profiles, said first set of profiles mapping totraces that run over a first axis of said sample and said sample stage,said traces having a recognized spacing between one another along asecond axis of said sample and said sample stage; b) means for adjustingthe relative position of said traces to said sample so as to create asecond set of fringe line disturbances; c) means for measuring saidsecond set of interferometer fringe line disturbances against saidpre-determined measurement scale information in order to generate asecond set of profiles that describe the topography of said sample; andd) means for interleaving said first set of profiles and said second setof profiles to create a topography description of said sample having aresolution along said second axis that is smaller than said spacing. 18.The apparatus of claim 17 wherein said adjusting further comprisesmoving said sample stage.
 19. The apparatus of claim 17 furthercomprising means for storing said topography description.
 20. Theapparatus of claim 19 wherein said means for storing further comprisesmeans for storing into a volatile memory.
 21. The apparatus of claim 20wherein said means for storing further comprises means for storing intoa non-volatile memory.
 22. The apparatus of claim 17 further comprisingmeans for displaying said topography description on a screen so thatsaid topography description can be viewed.
 23. The apparatus of claim 17wherein said means for measuring a first set of interferometer fringeline disturbances further comprises: a) means for detecting said fringeline disturbances from an optical intensity pattern provided from adetector associated with said interferometer; and b) means for comparingthe shapes of said detected fringe line disturbances at their respectivelocations against said pre-determined measurement scale information toform said first set of profiles, said pre-determined measurement scaleinformation further comprising the shapes of said detected fringe linedisturbances at their respective positions when said fringe linedisturbances were undisturbed.
 24. The apparatus of claim 23 whereinsaid means for detecting said fringe line disturbances further comprisesmeans for detecting the relative minima within said optical intensitypattern.
 25. The apparatus of claim 23 further comprising means forcompressing the data from which said first set of profiles arecomprised.
 26. The apparatus of claim 17 wherein means for measuring afirst set of interferometer fringe line disturbances and said means formeasuring said second set of interferometer fringe line disturbances arethe same means.
 27. A method, comprising: detecting on a pixilateddetector interferometer fringe lines that map to a first set of tracesthat run over a sample placed on a sample stage; converting a first setof disturbances in said fringe lines into a first set of data thatdescribes said sample's height along said first set of traces, saidconverting comprising measuring one or more distances that said detectedinterferometer fringe lines move on said pixilated detector with a perpixel unit of sample height; moving said sample stage to cause saidfringe lines to map to a second set of traces that run over said sample;and, converting a second set of disturbances in said fringe lines into asecond set of data that describes said sample's height along said secondset of traces.
 28. The method of claim 27 further comprising combiningsaid first and second sets of data to form a third set of data thatdescribes said sample's height along said first and said second set oftraces.
 29. The method of claim 28 wherein the distance between a tracefrom said first set of traces and a trace from said second set of tracesis less than a distance along said sample between traces mapped fromneighboring lines of said fringe lines.
 30. The method of claim 27wherein said traces map to a first axis along said sample and saidsample stage is moved along a second axis of said sample that isorthogonal to said first axis.
 31. The method of claim 27 wherein saidfringe lines result from said interferometer having a tilted referencemirror.
 32. The method of claim 27 further comprising visually showingan image of said sample's topography from said first and second sets ofdata.
 33. The method of claim 27 wherein said fringe lines are detectedby detecting relative minima in an optical intensity pattern.
 34. Themethod of claim 27 wherein said interferometer comprises a lens tomagnify an image of said sample.
 35. A method, comprising: detectinginterferometer fringe lines that map to a first set of traces that runover a sample placed on a sample stage; converting a first set ofdisturbances in said fringe lines into a first set of data thatdescribes said sample's height along said first set of traces, saidconverting comprising measuring one or more distances that said detectedinterferometer fringe lines move on a pixilated detector with a perpixel unit of sample height; moving a tilted reference mirrorsubstantially along an axis along which light is directed to saidreference mirror by said interferometer to cause said fringe lines tomap to a second set of traces that run over said sample; and, convertinga second set of disturbances in said fringe lines into a second set ofdata that describes said sample's height along said second set oftraces.
 36. The method of claim 35 further comprising combining saidfirst and second sets of data to form a third set of data that describessaid sample's height along said first and said second set of traces. 37.The method of claim 36 wherein the distance between a trace from saidfirst set of traces and a trace from said second set of traces is lessthan a distance along said sample between traces mapped from neighboringlines of said fringe lines.
 38. The method of claim 35 wherein saidtraces map to a first axis along said sample and said sample stage ismoved along a second axis of said sample that is orthogonal to saidfirst axis.
 39. The method of claim 35 wherein said fringe lines resultfrom said interferometer having a tilted reference mirror.
 40. Themethod of claim 35 further comprising visually showing an image of saidsample's topography from said first and second sets of data.
 41. Themethod of claim 35 wherein said fringe lines are detected by detectingrelative minima in an optical intensity pattern.
 42. The method of claim35 wherein said interferometer comprises a lens to magnify an image ofsaid sample.